1. Field of the Invention
The present invention is directed to a method wherein an output signal sequence is formed from a digital input signal sequence and a reference sequence with adaptive filters, with a filter output signal that is as optimally matched to the respective filter reference signal being formed from a respective filter input signal and a filter reference signal.
2. Description of the Prior Art
Methods of the above type are utilized, for example, in telecommunication technology for echo compensation that is necessary given comparatively great distances to be bridged between two telecommunication terminal devices. The input signal arriving at the reception equipment is supplied both to the circuit known as a xe2x80x9chybridxe2x80x9d that feeds the arriving signal into the local loop of the reception equipment and the outgoing signal into the line, as well as to the input of an adaptive filter in the reception equipment. The output signal of the adaptive filter is subtracted from the outgoing signal fed into the linexe2x80x94in this case, the reference signal at the same timexe2x80x94, and the remaining difference, i.e. the error signal, is used for the adaptation of the coefficient of the adaptive filter.
As is known the prior art, a single finite input response filter, abbreviated as FIR filter, having a number of coefficients, adapted to the signal delay that occurs, is utilized for this purpose. Given a sampling rate of kHz, a few hundred coefficients are required, with the equation known as the xe2x80x9cLeast Squares Wiener-Hopfxe2x80x9d equation supplying the optimum coefficient set for such a filter. Since standard signal processors, however, have limited computing capability, only the gradient method is applied instead of the mathematically optimum xe2x80x9cLeast Squares Wiener-Hopfxe2x80x9d equation, since the gradient method requires less calculating outlay. This method, however, requires long training times and is not suitable for supplying an optimum result for each input value.
As a result of taking the current signal delay into consideration, further, the filters defined thereby exhibit significantly more coefficients than would be necessary for the approximation of the magnitude frequency response, i.e. they are over-defined and therefore tend to unstable behavior.
U.S. Pat. No. 5,657,349 (xe2x80x9cMethod and Apparatus Capable of Quickly Identifying an Unknown System With A Final Error Reducedxe2x80x9d) discloses that an unknown system can be identified with K adaptive filters, whereby K is a whole number greater than 1. An input signal is thereby applied to the unknown system, this input signal being subdivided into K sub-band signals using an analysis filter bank. Each of these K sub-band signals is subsequently under-sampled and applied to one of the K adaptive filters as filter input signal. Just like the input signal, the output signal of the unknown system is subdivided into K sub-band systems, each of these K sub-band signals is under-sampled and applied as filter reference signal to respectively one of the K adaptive filters. Each of the K adaptive filters calculates the difference between the filter reference signal and the filter input signal and emits this as the filter output signal, this being utilized for the adaptation of the filter coefficient. The filter output signals are subsequently over-sampled and combined to form an output signal using a synthesis filter bank.
If a pseudocode is then employed for the input signal and a payload signal affected with an echo is provided as output signal of the unknown system, then an echo-suppressed payload signal is present at the output of the synthesis filter bank. The extent of the echo suppression is essentially dependent on the coefficients of the adaptive filters.
The quality of the output signal, however, is also dependent on the division of the overall frequency spectrum into sub-bands, with a finer subdivision supplying a qualitatively better signal. Since the sub-division is made in frequency bands of equal width, a relatively slight quality improvement is achieved at the expense of a technically and computationally large outlay.
An object of the present invention is to provide a method for filtering a digital filter sequence wherein the filtering ensues with comparatively little technical and computational outlay.
This object is inventively achieved in a method wherein time functions are formed from the digital input signal sequence and the digital reference sequence with scaling functions, respective component sets are determined from the time functions using discrete parameter wavelet transformation, applied in pairs to adaptive filters as a filter input and a filter reference signal, and wherein the filter output signals of the adaptive filters are combined to form a single output signal sequence using an operation inverse to the originally applied discrete parameter wavelet transformation.
In contrast to the conventional methods, in the inventive method contradictory demands need not be met for the approximation of the magnitude of frequency response and for taking the signal delay into consideration. This is distinguished by especially small filter lengthsxe2x80x94i.e., by few coefficientsxe2x80x94and, thus, substantially less computational outlay for determining the optimum coefficient set for the filters employed.
The division of the frequency spectrum of the input signal in the inventive method, moreover, ensues in logarithmic scale with respect to the center frequency of the individual frequency bands. The employment of wavelets advantageously offers a uniform quality for the individual frequency bands. An increase in the quality of the output signal sequence therefore can ensue with comparatively little technical and computational outlay.
In an embodiment of the inventive method the output signal sequence xcex5(nxe2x88x92p) is reconstructed instead of the output signal sequence y(nxe2x88x92p), namely from the error sequences dn1(e),dn2(e), . . . ,dnL(e) and cnL(e). This method, for example, is utilized for the application known as xe2x80x9cinterference cancelingxe2x80x9d. A noise-infested payload signal is thereby supplied to the adaptive filters the as filter reference signal and a noise correlated thereto is supplied as the filter input signal. Since the adaptive filters are designed for adapting the filter output signal to the filter reference signal, the noise is present as the filter output signal and the nearly noise-compensated payload signal is present as the error signal.
In an embodiment of the inventive method the factors dn1(x),dn2(x), . . . ,dnL(x) and cn1(x), or, respectively, dn1(r),dn2(r), . . . ,dnL(r) and cnL(r) of the discrete parameters of wavelet transformation are determined according to the Mallat algorithm for multi-resolution analysis, and the output signal sequence y(nxe2x88x92p) or xcex5(nxe2x88x92p) is reconstructed with the inverse operation, the Mallat algorithm for the multi-stage synthesis, being reconstructed from the factors dn1(y),dn2(y), . . . ,dnL(y) and cnL(y). The Mallat algorithm for the multi-resolution analysis, which is disclosed in Mallat, S. G., A Theory For Multi resolution Signal Decomp.: The Wavelet Representation; IEEE Trans. Pattern Analysis, Machine Intelligence, Vol. 11, No. 7, pp. 674-693, July 1989, makes the method of making discrete parameter wavelet transformation, abbreviated as DPWT, available for practical application with digital signal processors and comparatively little technological outlay. Modules are needed for this purpose that are composed of a finite impulse response low-pass filtering (FIR low-pass filter) and immediately successively ensuing under-sampling by the factor of two, and modules that are composed of a finite impulse response high-pass filtering (FIR high-pass filtering) and immediately successively ensuing under-sampling by the factor of two. The Mallat algorithm for multi-stage synthesis that is described in Chan, Y. T., Wavelet Basics, Kluwer Academic Publishing Group 1995, requires modules that are composed of an over-sampling by the factor of two and immediately subsequently ensuing FIR low-pass filtering and modules that are composed of an over-sampling by the factor of two and immediately successively ensuing FIR high-pass filtering. The absolute values of the coefficients of all low-pass and high-pass filters employed are identical. Differences in the sequencing and the operational sign of the respective absolute values of the coefficient sets merely occur between the different types of filter, so that a common coefficient set can be employed for all filters, and, thus memory location can be saved.
Due to the recursive under-sampling by the factor of two, a comparatively high, possible signal delay can occur and above this between the individual stages, even given a filter length that is adapted to the approximation of the amount frequency response. It is especially advantageous that the number of required calculating steps, which is calculated as   n  =                    n        0            +                        n          0                2            +                        n          0                4            +      …        =          2      ·              n        0            
where n0 references the number of calculating steps in the first stage, is significantly lower compared to a single, long FIR filter. The recited equation is valid under the pre-condition that all filters have the same length which is not necessary for the inventive method.
It is also beneficial when the coefficients of the FIR filters g(l),h(l),{overscore (g)}(l),{overscore (h)}(l) l=0,1, . . . ,pxe2x88x921 utilized in the framework of the Mallat algorithm for the multi-resolution analysis and the multi-stage synthesis agree with the values defined by I. Daubechies, whereby pxe2x88x921 indicates the filter order. This class of wavelets, which is known from Daubechies, I, Orthonormal Basis of Compactly Supported Wavelets, Comm. In Pure and Applied Math, Vol. 41, No. 7, pp. 909-996, 1988, offers good resolution in the time domain as well as in the frequency domain. The wavelets, moreover, are temporally exact and are limited in the frequency domain by a rapidly dropping spectrum at low and high frequencies.
In a further embodiment of the invention the least mean square algorithm is employed for the operation of the adaptive filters. This algorithm supplies the optimum coefficient set for a FIR filter.